This work is devoted to the study of relativistic anisotropic compact objects. To obtain this class of solutions of the Einstein field equations, we have developed a general scheme to generate the metric of the space–time describing the interior of the compact structure. This approach is based on the class I space–time and the extended gravitational decoupling by means of an extended geometric deformation (EGD). The class I condition provides a differential equation relating both metric potential \(\nu \) and \(\lambda \), whilst the EGD translates the metric potentials to \( \nu =\xi +\beta \,h(r)\) and \( \lambda =-\ln [\mu +\beta \,f(r)]\), where h(r) and f(r) are the deformation functions and \(\beta \) a dimensionless constant. In this case the pair \(\{\xi ,\mu \}\) represents the seed solution satisfying the class I condition without any deformation. Once the deformed metric potentials are inserted into the class I, the main task is to obtain h(r) or f(r). So, in this case a particular ansatz for h(r) is considered in conjunction with \(\beta =0.5\) to get f(r). In order to check feasibility of our model, we have performed a thoroughly physical, mathematical and graphical analysis.

这项工作致力于相对论各向异性紧凑物体的研究。为了获得爱因斯坦场方程的此类解决方案，我们开发了一种通用方案来生成描述紧凑结构内部的时空度量。这种方法基于I类时空，并通过扩展的几何变形（EGD）进行扩展的重力解耦。I类条件提供了一个与度量电势\（\ nu \）和\（\ lambda \）相关的微分方程，而EGD将度量电势转换为\（\ nu = \ xi + \ beta \，h（r） \）和\（\ lambda =-\ ln [\ mu + \ beta \，f（r）] \），其中h（r）和f（r）是形变函数，\（\ beta \）是无量纲常数。在这种情况下，对\（\ {\ xi，\ mu \} \）表示满足I类条件且没有任何变形的种子解。一旦将变形的度量电势插入到I类中，主要任务就是获得h（r）或f（r）。因此，在这种情况下，考虑将h（r）的特定ansatz与\（\ beta = 0.5 \）结合使用以获得f（r）。为了检查模型的可行性，我们进行了彻底的物理，数学和图形分析。